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Income taxes - Significant Portions of Deferred Tax Assets and Liabilities (Details) - USD ($)
$ in Millions
Dec. 31, 2017
Dec. 31, 2016
Deferred tax assets    
Tax loss carryforwards $ 837.6 $ 889.6
Postretirement benefits 437.7 728.9
Foreign tax credit carryforwards 127.0 317.6
Other tax credit carryforwards 29.1 91.4
Deferred revenue 40.9 81.0
Employee benefits and compensation 35.2 49.1
Purchased capitalized software 22.2 32.6
Depreciation 24.5 28.3
Warranty, bad debts and other reserves 5.3 16.1
Capitalized costs 3.1 10.9
Other 39.3 27.7
Total deferred tax assets, gross 1,601.9 2,273.2
Valuation allowance (1,441.1) (2,084.6)
Total deferred tax assets 160.8 188.6
Deferred tax liabilities    
Capitalized research and development 24.3 20.3
Other 25.8 28.4
Total deferred tax liabilities 50.1 48.7
Net deferred tax assets $ 110.7 $ 139.9